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Suppose you wanted to do a time-resolved experiment with a molecular beam traveling at, say, 300 m/s involving a mobile excitation (pump) laser that scans across the length of the molecular beam and a stationary detector. So the time-resolution of the experiment depends on how precisely the position of the excitation laser can be fine-tuned, e.g. if the laser can be tuned in the millimeter range, then the time resolution would be in the microsecond time scale. (Don't worry about the path length of the beam to the detector. It's reasonable to imagine that one would be interested in obtaining ns accuracy for a system in which nothing happens for several ms). Also suppose that the velocity distribution of the particles in the beam have a sharp velocity distribution, such that ∆v/v≈0.01. My question is, then, to what degree of accuracy can the excitation laser's position be fine-tuned using modern optics? Obviously the intensity, wavelength, and type of laser will have some effect on the answer, but I'm interested in a ballpark figure anyway. The obvious follow-up question is how, experimentally, does one tune the laser to that level of accuracy? Would relativistic effects start to be an issue at some point? And is the velocity distribution (or, for that matter, the measurement of the velocity) actually going to end up being the limiting factor on time resolution in the end?

Thanks in advance for your answers.

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Do you need the beam to maintain coherence or do you simple need a very bright light? //trying to recall exactly how the coherence conditions get used to set geometric constraints... –  dmckee Dec 7 '10 at 16:46
    
@dmckee: Probably not. The detector in this type of experiment is usually a mass spectrometer or a bolometer. –  David Hollman Dec 7 '10 at 17:10
    
As a side-note, if you want good time resolution, the best tool to use are pulsed laser. But femtosecond lasers are more expensives than continuous ones ... –  Frédéric Grosshans Dec 7 '10 at 17:56
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The resolution would ultimately depend on the size of the laser beam where it crosses the molecular beam. The smallest size you'll be able to obtain with the beam is on the order of the optical wavelength (there are some numerical factors that depend on the exact geometry, but if you're just looking for a ballpark figure, that will give you a lower bound).

The accuracy you can get with the physical position pretty much depends on how much money you're willing to spend. Small fractions of a millimeter are pretty trivial, and can be done with fairly ordinary optical mounts-- people doing cold-atom experiments routinely manage to hit micron-scale clouds of atoms with micron-sized laser beams just using optical mounts from ThorLabs. (It takes some patience, but it's not a major technical challenge.)

If you're operating in the infinite money limit, you can get commercial position systems that will give you nanometer-ish accuracy over a fairly wide range of positions-- I think I've seen claims of being able to position some object within 100nm over a span measured in meters. That'll cost you big money, though, and is probably complete overkill.

In any case, I suspect that the velocity spread and beam size will be the ultimate limiting factors. If your laser beam is 600 nm wide and the speed is 300 m/s, that corresponds to an uncertainty of a couple of nanoseconds, which is a distance uncertainty of a few hundred nm. Positioning accuracy much better than a micron isn't going to make much difference in that case.

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Thanks! That's exactly what I wanted to know. I didn't think about the fact that the wavelength would be another limiting factor anyway. –  David Hollman Dec 7 '10 at 17:18
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